In this paper, we lay the foundations of the theory of slice regular functions in several (non-commuting) variables ranging in any real alternative $^*$-algebra, including quaternions, octonions and Clifford algebras. This higher dimensional function theory is an extension of the classical theory of holomorphic functions of several complex variables. It is based on the construction of a family of commuting complex structures on $mathbb R^{2^n}$. One of the relevant aspects of the theory is the validity of a Cauchy-type integral formula and the existence of ordered power series expansions. The theory includes all polynomials and power series with ordered variables and right coefficients in the algebra. We study the real dimension of the zero set of polynomials in the quaternionic and octonionic cases and give some results about the zero set of polynomials with Clifford coefficients. In particular, we show that a nonconstant polynomial always has a non empty zero set.
Slice regular functions in several variables / Perotti, Alessandro; Ghiloni, Riccardo. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 2022:(2022). [10.1007/s00209-022-03066-9]
Scheda prodotto non validato
I dati visualizzati non sono stati ancora sottoposti a validazione formale da parte dello Staff di IRIS, ma sono stati ugualmente trasmessi al Sito Docente Cineca (Loginmiur).
Titolo: | Slice regular functions in several variables | |
Autori: | Perotti, Alessandro; Ghiloni, Riccardo | |
Autori Unitn: | ||
Titolo del periodico: | MATHEMATISCHE ZEITSCHRIFT | |
Anno di pubblicazione: | 2022 | |
Codice identificativo WOS: | WOS:000535360700024 | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00209-022-03066-9 | |
Handle: | http://hdl.handle.net/11572/346219 | |
Citazione: | Slice regular functions in several variables / Perotti, Alessandro; Ghiloni, Riccardo. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 2022:(2022). [10.1007/s00209-022-03066-9] | |
Appare nelle tipologie: | 03.1 Articolo su rivista (Journal article) |